{"paper":{"title":"On the Mortality Problem: from multiplicative matrix equations to linear recurrence sequences and beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DM","authors_text":"Igor Potapov, Paul C. Bell, Pavel Semukhin","submitted_at":"2019-02-26T20:03:52Z","abstract_excerpt":"We consider the following variant of the Mortality Problem: given $k\\times k$ matrices $A_1, A_2, \\dots,A_{t}$, does there exist nonnegative integers $m_1, m_2, \\dots,m_t$ such that the product $A_1^{m_1} A_2^{m_2} \\cdots A_{t}^{m_{t}}$ is equal to the zero matrix? It is known that this problem is decidable when $t \\leq 2$ for matrices over algebraic numbers but becomes undecidable for sufficiently large $t$ and $k$ even for integral matrices.\n  In this paper, we prove the first decidability results for $t>2$. We show as one of our central results that for $t=3$ this problem in any dimension i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10188","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}